Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Map;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int a = in.nextInt();
            int b = in.nextInt();

            double v[] = new double[n];
            Map<Double, Integer> vc = new HashMap<>();
            for (int i = 0; i < n; i++) {
                v[i] = in.nextDouble();
                vc.put(v[i], vc.getOrDefault(v[i], 0) + 1);
            }

            Arrays.sort(v);
            double mean = 0;
            for (int i = n - 1; i >= n - a; i--)
                mean += v[i];
            mean /= a;
            out.println(mean);

            int r = 1;
            for (int i = n - a - 1; i >= n - b; i--) {
                if (v[i] != v[n - a])
                    continue;
                r++;
            }
            int s = 1;
            for (int i = n - a + 1; i < n; i++) {
                if (v[i] != v[n - a])
                    continue;
                r++;
                s++;
            }
            long count = 0;
            if (v[n - a] != v[n - 1]) {
                count = 1;
                for (int i = 1; i <= s; i++) {
                    count *= vc.get(v[n - a]) - i + 1;
                    count /= i;
                }
            } else {
                for (int cr = s; cr <= r; cr++) {
                    long cc = 1;
                    for (int i = 1; i <= cr; i++) {
                        cc *= vc.get(v[n - a]) - i + 1;
                        cc /= i;
                    }
                    count += cc;
                }
            }
            // out.println("AC")
            out.println(count);
        }

    }

    static class FastScanner {
        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int bufPointer;
        private int bufLength;

        public FastScanner(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (bufPointer >= bufLength) {
                if (bufLength == -1)
                    throw new InputMismatchException();

                bufPointer = 0;
                try {
                    bufLength = in.read(buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (bufLength <= 0)
                    return -1;
            }
            return buffer[bufPointer++];
        }

        private static boolean isPrintableChar(int c) {
            return c >= 33 && c <= 126;
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            StringBuilder sb = new StringBuilder();

            int b = readByte();
            while (!isPrintableChar(b))
                b = readByte();

            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }

            return sb.toString();
        }

        public long nextLong() {
            long n = 0;

            int b = readByte();
            while (isSpaceChar(b))
                b = readByte();

            boolean minus = (b == '-');
            if (minus)
                b = readByte();

            while (b >= '0' && b <= '9') {
                n *= 10;
                n += b - '0';
                b = readByte();
            }

            if (!isSpaceChar(b))
                throw new NumberFormatException();

            return minus ? -n : n;
        }

        public int nextInt() {
            long n = nextLong();

            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE)
                throw new NumberFormatException();

            return (int) n;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}